I actually don't mind betting here at all.
If he's unpaired or has a low PP we can get him to fold and he's passive so I don't like taking an "induction" line because he simply won't fall for it enough and I'm certainly not taking K7s to SD here vs him if he bets the river. if he was bluffing at the flop then we take it down, that's fine, we weren't showing down anyway so the concept of "getting better hands to fold" falls behind "winning the pot" in importance.
If called on the turn the river's tricky as the obvious draw completed but I would expect him to donk a made flush for fear you'd check behind.
If bet into it's a pretty clear fold
If checked to the question becomes can we get him off a small pair so it comes down to "Do you believe 33% of the time he has a small PP he's willing to fold here when he checks?". Given the river also completes some sets and straights I don't think there are enough combos we can get him off here but then again our hand may seem like it has SD value but on that river it has none vs his turn peeling range. If we check behind we're giving up.
This may be a very rare situation but I may just bet here thinking we pretty much never have the best hand and a decent % of the time he's going to have a pair he's played passively and go "ugh everything completed and there's an Ace on board and he's bet 2 streets when I checked, guess I should fold my pair" which isn't a terrible thought process.